GCF of 5295/213, 8214/5756
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5295/213, 8214/5756 i.e 3/1226028 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5295/213, 8214/5756.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 5295/213,8214/5756?
Given fractions are 5295/213,8214/5756
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 5295/213,8214/5756, numerators are 5295,8214
Denominators are 213,5756
The GCF of 5295,8214 is 3 .
LCM of 213,5756 is 1226028.
The greatest common factor of 5295/213,8214/5756 = [GCF of 5295,8214]/[LCM of 213,5756]= 3/1226028
Therefore, the GCF of 5295/213,8214/5756 is 3/1226028.
To find the highest common factor of 5295,8214, we have to find the factors of both numbers and list the highest common factor.
The factors of 5295 are 1, 3, 5, 15, 353, 1059, 1765, 5295
The factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214
The HCF of 5295,8214 is 3.
Lets's calculate GCF of 5295,8214
| 3 | 5295, 8214 |
| 1765, 2738 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 5295,8214 By Matching Biggest Common Factor Method
Now, list down the factors of 5295
:1,3,5,15,353,1059,1765,5295
Now, list down the factors of 8214
:1,2,3,6,37,74,111,222,1369,2738,4107,8214
Greatest Common Factor
We found the factors 5295,8214 . The biggest common factor number is the GCF number.
So the greatest common factor 5295,8214 is 3.
Lets's calculate LCM of 213,5756
Given numbers has no common factors except 1. So, there LCM is their product i.e 1226028
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1226028
Therefore, the GCF of Fractions 5295/213,8214/5756 is 3/1226028
Least Common Multiple of 213,5756 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 213,5756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,5756) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(213,5756) x common factors =1 x 1 = 1
LCM(213,5756) = ( 213 × 5756 ) / 1
LCM(213,5756) = 1226028 / 1
LCM(213,5756) = 1226028
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FAQs on GCF of Fractions of 5295/213, 8214/5756
1. What is the HCF of 5295,8214?
The HCF of 5295,8214 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 5295/213, 8214/5756?
Answer: GCF of Numerators as per given numbers 5295/213, 8214/5756 is
GCF of Numerators i.e. for 5295,8214 is 3
LCM of denominators i.e. for 213,5756 is 1226028.
Thus, GCF of Fractions is 3/1226028.Finally, GCF of Fractions for 5295/213, 8214/5756 is 3/1226028.